Progress in Fractional Differentiation & Applications

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In this work, we presented the numerical investigation on the dynamics of fractional Langevin equation which is driven by a fractional Brownian motion and Caputo-Fabrizio fractional derivative operator were utilized. The order of fractional derivative was considered to be ν = 2 − 2H , where H ∈ (1/2, 1) is the Hurst’s index. In the context of numerical schemes, we present different numerical approaches such as the discrete sequence of finite difference, to simplify the second-order ordinary derivative, while for the fractional derivative term, we presented the discrete approximation using simple quadrature formula. Additionally, for overdamped case (without inertial term), we used the Adams-Bashforth method corresponding to the Caputo-Fabrizio fractional derivative. The convergence and stability analysis of the obtained numerical solution were established in this study.

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